Low‐Frequency Reconstruction for Full Waveform Inversion by Unsupervised Learning.

Obtaining reliable low‐frequency seismic data is crucial for effectively reducing cycle‐skipping in full waveform inversion. However, acquiring high signal‐to‐noise ratio low‐frequency information from field data remains a challenge. An effective solution to mitigate cycle‐skipping is to utilize low‐frequency information synthesized by neural networks to obtain low‐wavenumber initial models. Previous attempts to reconstruct synthetic low‐frequency data using supervised learning methods have shown feasibility but were limited to training with synthetic data that required labeled information. In this study, we employed an unsupervised learning method, namely cycle‐consistent adversarial networks (CycleGAN), to reconstruct large‐scale‐feature related low‐frequency information based on the high‐frequency input data. Unlike supervised learning, CycleGAN allows the use of field data as input to train the network, which is more closely aligned with practical applications. Nevertheless, this approach presents challenges in terms of training complexity and potential output stability. To overcome these challenges, we reconstructed an appropriate target data set that combines high, medium, and low‐frequency components and incorporated additional loss functions to enhance the network's output performance. We conducted quantitative evaluations of the method's sensitivity to the target data set and its ability to handle low‐quality input data through numerical testing. The final results from field data testing confirmed the feasibility and effectiveness of the proposed method. Plain Language Summary: Full waveform inversion (FWI) is a state of art imaging technology, but missing low‐frequency energy in active seismic waveform leads to FWI failure on field data. To address this challenge, we used cycle‐consistent adversarial networks (CycleGAN), an unsupervised learning method, to generate missing low‐frequency information from high‐frequency field data. Unlike supervised learning methods that require labeled synthetic data, CycleGAN can directly use real‐world field data for training, making it more practical. We enhanced the method by constructing a suitable target data set to improve the network's performance. The field data test confirmed the effectiveness of our approach in reducing mismatch caused by large discrepancies between observed and synthesized data and improving subsurface imaging. Key Points: Low‐frequency data can help alleviate the issue of cycle‐skipping in full‐waveform inversionWe utilize unsupervised learning with field data as input to train the network for predicting relevant low‐frequency informationSwitching from a single low‐frequency target data set to a composite high‐medium‐low frequency form improves the network's performance [ABSTRACT FROM AUTHOR]